Bohdan Macukow

Factorization of the transfer matrix for symmetrical optical systems

In the paraxial approximation a symmetrical optical system may be represented by a 2 × 2 matrix. It has been the custom to describe each optical element by a transfer matrix representing propagation between the principal planes or through an interface for thin elements. If the focal-plane representation is used instead, any focusing element or combination of elements is represented by the same antidiagonal matrix whose nonzero elements are the focal lengths: The matrix represents propagation between the focal planes. For propagation between any two arbitrary planes, the system transfer matrix can be decomposed into the product of two upper triangular matrices and an antidiagonal matrix. This decomposition yields the above-mentioned focal-plane matrix, and the two upper triangular matrices represent propagation between the input and the output planes and the focal planes. Because the matrix decomposition directly yields the parameters of interest, the analysis and the synthesis of optical systems are simpler to carry out. Examples are given for lenses, diopters, mirrors, periodic sequences, resonators, lenslike media, and phase-conjugate mirror systems.

Optical associative memory model based on neural networks having variable interconnection weights

A new model is proposed for a content-addressable memory (CAM) based on neural networks. Like the previous Hopfield model, the information is stored in the structure of the network and the read-out procedure may be implemented in the form of an optical vector-matrix multiplier. This model introduces intermediate layers of interneurons between the neuron layers and a dependence of the interconnection weights to a given neuron on the previous history of the neuron. The storage prescription allows each matrix element to have three values instead of only two as in the previous Hopfield model. This more complex model gives better results than the Hopfield model.

Matrix decompositions for nonsymmetrical optical systems

A new approach to the representation of nonsymmetrical optical systems by matrices is introduced. In the paraxial approximation each component of an optical system is represented by a 4 × 4 unitary matrix, and the product of those matrices yields the transfer matrix of the system. The transfer matrix that represents the propagation between two arbitrary planes through the system containing two independently rotated cylindrical lenses is decomposed into the product of three matrices. The eigenvalues of the submatrices in this factorized form determine the focal lengths of the equivalent system and the localization of the foci of the system with respect to these arbitrarily chosen planes.

Counter‐propagation neural network for image compression

Recently, several image compression techniques based on neural network algorithms have been developed. In this paper, we propose a new method for image compression—the modified counterpropagation neural network algorithm, which is a combination of the selforganizing map of Kohonen and the outstar structure of Grossberg. This algorithm has been successfully used in many applications. The modification presented has also demonstrated an interesting performance in comparison with the standard techniques. It was found that at the learning stage we can use any image for a network training (without a significant influence on the net operation) and the compression ratio and quality depend on the size of the basic element (the number of pixels in the cluster) and the amount of error tolerated when processing.

Heat Consumption Prediction with Multiple Hybrid Models

Load forecasting plays an important role in modern utilities. However, further improvements can be expected by predicting the load at a consumer level. The latter approach has become available with the advent of low-cost monitoring and transmission systems. Still, due to the limited number of monitored clients, the way groups of consumers should be identified and whether their data is sufficient for high quality prediction models remains an open issue. The work summarises the results of building prediction models for different consumer groups of a district heating system. The way self-organising maps, multilayer perceptrons and simple prediction strategies can be applied to identify groups of consumers and build their prediction models has been proposed. The hypothesis that a billing database enables group identification has been verified. Significant improvements in prediction accuracy have been observed.

Neural Network Model For Fast Learning And Retrieval

An approach to learning in a multilayer neural network is presented. The proposed network learns by creating interconnections between the input layer and the intermediate layer. In one of the new storage prescriptions proposed, interconnections are excitatory (positive) only and the weights depend on the stored patterns. In the intermediate layer each mother cell is responsible for one stored pattern. Mutually interconnected neurons in the intermediate layer perform a winner-take-all operation, taking into account correlations between stored vectors. The performance of networks using this interconnection prescription is compared with two previously proposed schemes, one using inhibitory connections at the output and one using all-or-nothing interconnections. The network can be used as a content-addressable memory or as a symbolic substitution system that yields an arbitrarily defined output for any input. The training of a model to perform Boolean logical operations is also described. Computer simulations using the network as an autoassociative content-addressable memory show the model to be efficient. Content-addressable associative memories and neural logic modules can be combined to perform logic operations on highly corrupted data.

Interpreting tree-based prediction models and their data in machining processes

Machine-learning techniques frequently predict the results of machining processes, based on pre-determined cutting tool settings. By doing so, key parameters of a machined product can be predicted before production begins. Nevertheless, a prediction model cannot capture all the features of interest under real-life industrial conditions. Moreover, careful assessment of prediction credibility is necessary for accurate calibration; aspects that should be addressed through appropriate modeling and visualization techniques. A machine process test problem is proposed to analyze data-visualization techniques, in which a real data set is analyzed that describes deep-drilling under different cutting and cooling conditions. The main objective is the efficient fusion of visualization techniques with the knowledge of industrial engineers. Common modeling and visualization techniques were first surveyed, to contrast standard practice with our novel approach. A hybrid technique combining conditional inference trees with dimensionality reduction was then examined. The results show that a process engineer will be able to estimate overall model accuracy and to verify the extent to which accuracy depends on industrial process settings and the statistical significance of model predictions. Moreover, evaluation of the data set in terms of its sufficiency for modeling purposes will help assess the credibility of these decisions.

Education quality assurance in the Warsaw University of Technology - prerequisites and activities already undertaken

The last few years have seen intensive time invested in the discussions concerning quality assessment and quality improvement within the Polish university sector. There is limited experience of formalized quality assessment in the higher education sector in Poland, and several pilot projects have been running that represent a first step in establishing a general methodology, rules, procedures and, finally, system. In recent years the Warsaw University of Technology has been involved in some projects, mainly under the Tempus Programme. An essential element of quality assurance and quality assessment is that of benchmarking against international best practice; then our EU partners were visited. Data on existing quality management procedures and tools were collected and compiled, creating the background for future discussions and decisions. This year we started a new project(together with the Technical University of Lodz), devoted to quality issues - and precisely to the introduction of an internal quality education system in our universities. This paper outlines the previous results, but mainly the activities that will be carried out in the next two years to achieve the projects objective - establishment of a university quality assurance unit and introduction of a quality assurance system.

Methods of artificial intelligence in blind people education

This paper presents the idea of recognition of music symbols to help the blind people reading music scores and operating music notation. The discussion is focused on two main topics. The first topic is the concept of the computer program, which recognizes music notation and processes music information while the second is a brief presentation of music processing methods including recognition of music notation – Optical Music Recognition technology – based on artificial neural networks. The short description and comparison of effectiveness of artificial neural networks is also given.

Beyond Pattern Recognition With Neural Nets

Neural networks are finding many areas of application. Although they are particularly well-suited for applications related to associative recall such as content-addressable memories, neural nets can perform many other applications ranging from logic operations to the solution of optimization problems. The training of a recently introduced model to perform boolean logical operations such as XOR is described. Such simple systems can be combined to perform any complex boolean operation. Any complex task consisting of parallel and serial operations including fuzzy logic that can be described in terms of input-output relations can be accomplished by combining modules such as the ones described here. The fact that some modules can carry out their functions even when their inputs contain erroneous data, and the fact that each module can carry out its functions in parallel with itself and other modules promises some interesting applications.